ChineseRemainder

ChineseRemainder[{r1,r2,},{m1,m2,}]

gives the smallest with that satisfies all the integer congruences .

ChineseRemainder[{r1,r2,},{m1,m2,},d]

gives the smallest with that satisfies all the integer congruences .

Details

  • If no solution for exists, ChineseRemainder returns unevaluated.
  • If all 0ri<mi, then the result satisfies .
  • ChineseRemainder[{r1,r2,},{m1,m2,}] gives a solution with .
  • ChineseRemainder[{r1,r2,},{m1,m2,},d] gives a solution with .

Examples

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Basic Examples  (2)

The smallest positive integer that satisfies and :

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Out[1]=

Find the smallest positive integer giving remainder when divided by :

In[1]:=
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Out[1]=

Applications  (3)

Properties & Relations  (1)

Possible Issues  (1)

See Also

Reduce  FindInstance  GCD

Tutorials

Introduced in 2007
(6.0)
| Updated in 2016
(11.0)